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Can you strip down the file to a minimum repro case?
Remove half the layers and see if the PSD Plugin can load it. If it loads successfully, then the problem was in one of the layers that was deleted. If it still doesn't load, then the problem can be found in one of the layers that remains. Keep halving the layers until you're down to one, and then erase the contents of the layer.
The error message indicates a parsing error, so I don't need to look at the contents of the file. The image can be blank. As long as the file still fails to load in the PSD Plugin, I can take a look at the structure of the file to see what's causing it.

Please send me a copy of the PSB file that causes this error. If the file is too large to email, please upload it to OneDrive and share it to me.
My email address is at the top of the PSD Plugin website: https://www.psdplugin.com/

There is not enough information yet to diagnose the problem.
Please post screenshots of File Explorer, opened to the following directories. Use Detail mode, and maximize the window so we can see filesize and timestamp.
C:\Program Files\paint.net
C:\Program Files\paint.net\Effects
C:\Program Files\paint.net\FileTypes

This is not a common error message. Please send me the PSD file so I can investigate the problem further. Use the email address at the top of the PSD Plugin web page: https://www.psdplugin.com/
If the file is larger than about 20 MB, please upload it to OneDrive instead and share it with me using that email address.

We need some more information to diagnose this problem.
Please post screenshots of Windows Explorer, opened to the following directories. Use Detail mode, and maximize the window so we can see filesize and timestamp.
C:\Program Files\paint.net
C:\Program Files\paint.net\Effects
C:\Program Files\paint.net\FileTypes

It would be 164,771,712 bytes if the file has one layer.
PSD files can contain thousands of layers, so that file could require hundreds of GB of memory to load into Paint.NET.
The problem is that Photoshop has partial layers and Paint.NET doesn't. Because layers are cheap in Photoshop, graphic designers can use layers like candy. They'll create a new layer for a 10x10 image element. When the file is loaded into Paint.NET, that 10x10 layer turns into a full 3892 x 3528 layer.

Codeplex has finally taken action, and files can now be downloaded successfully on Chrome and Firefox.
Due to the quick reporting from users, the PSD Plugin was one of the first projects on Codeplex to workaround the problem. I also have reason to believe that the operators of Codeplex took action based directly on my recommendations. Therefore, every project on Codeplex owes a debt of gratitude to the users of the PSD Plugin. Thank you!

There is currently a URL block in effect against all downloads on Codeplex. The file checks out with a clean bill of health on VirusTotal.com.
I have placed a link to the alternate download site on the PSD Plugin Codeplex page, and I have reported the problem to the people who run Codeplex.
Since it is a URL block, that's about all I can do. Google requires the operator of the website (Microsoft) to get in touch with them to get the block lifted.

It has come to my attention that Codeplex downloads are being blocked in many browsers, including Chrome. Every download on Codeplex.com is being blocked -- even Microsoft programs like the Windows USB/DVD Download Tool!
If you are running Windows 10, the Edge browser can still download the PSD Plugin successfully. If you are not using Windows 10, you can download the latest version of the PSD Plugin here: http://www.psdplugin.com/

In addition to cleaning out your Effects folder, please also clean out your FileTypes folder:
In Windows Explorer, go to C:\Program Files\paint.net\Effects
Delete all files.
Take a screenshot here.
In Windows Explorer, go to C:\Program Files\paint.net\FileTypes
Delete all files.
Take a screenshot here.
If Windows cannot delete any files, restart the computer and try again.
Next, make sure that the old version of the PSD Plugin is actually gone:
Start Paint.NET.
File-Open
Click the dropdown for "All image types"
Take a screenshot here.
Make sure that "Photoshop (*.psd)" does NOT appear on the dropdown list.
Exit Paint.NET.
Finally, follow these steps to download and install the new version of the plugin: https://psdplugin.codeplex.com/wikipage?title=Installation
Follow each step exactly, even if you normally do the same thing in a different way. These steps have been tested by many users who initially had difficulty installing the plugin, and they are known to work on Windows 7 through Windows 10.

Windows Defender does not alert on PSDPlugin-2.5.0.zip. VirusTotal also gives it a clean bill of health at 55 different malware scanners: https://www.virustotal.com/en/file/309c44f2ceec555b0efddda81679a54a0bb89fccc38b784cc4c8609e87e4327e/analysis/
The problem may be caused by a browser add-on. I would suggest using a different web browser to download the plugin. Windows 10 Edge would be a good choice because it has very few add-ons available. However, any web browser will do except the one that you normally use. Make sure to copy-paste the direct link to the download: http://psdplugin.codeplex.com/downloads/get/1606282
If you continue to have this problem even with a different web browser, please do NOT delete the file. Submit the file to VirusTotal for analysis, and post the URL here.

The timestamp check is actually not just to verify the file version, but also to check for side effects. As we saw above, third-party ZIP tools can have trouble with things that work correctly using the Windows built-in ZIP handler.
The built-in ZIP handler in Windows always extracts files with the time set to the local time zone. No matter which time zone the user is in, the same times will be displayed in Windows Explorer. I just tried with my system set to Cyprus time (Eastern European time zone), and it shows the correct time.

Those errors only appear if you have PSD Plugin 2.4.1 or earlier installed. If it is showing up, then PSD Plugin 2.5.0 is not installed properly
People seem to be having trouble because upgrading requires that the old version be overwritten. You don't have to do this on fresh installs, so this problem doesn't come up.
The best workaround is to first delete the old version:
Restart the computer.
Delete Photoshop.dll from C:\Program Files\paint.net\FileTypes
Start Paint.NET and make sure that it cannot open or save PSD files.
Close Paint.NET.
Once this has been done, you can then do a fresh install of PSD Plugin 2.5.0:
Download a fresh copy of PSD Plugin 2.5.0 from: http://psdplugin.codeplex.com/downloads/get/1606282
Right-click the ZIP file and select "Extract All ..."
Make sure PhotoShop.dll has the timestamp: 9/11/2016 10:35 PM
Copy PhotoShop.dll into C:\Program Files\paint.net\FileTypes

DanceERB sent me email separately with the error message. I am posting here so that you're not left in suspense about the resolution.
The problem was caused by using 7-Zip to extract Photoshop.dll directly into C:\Program Files\paint.net\FileTypes. This folder requires administrative privileges to write to it. However, 7-Zip runs as an unprivileged user and does not try to elevate itself to admin. It just gives an error message.
The workaround is to do a two-stage copy. First, use 7-Zip to extract the ZIP file to another directory. Then use Windows Explorer to copy the DLL into C:\Program Files\paint.net\FileTypes. Windows Explorer will prompt to elevate, so the second copy operation will work.
Incidentally, this is the sort of corner case that third-party utilities often miss. The ZIP handler that's built-into Windows will prompt to elevate if the user does not have permission to write to a directory.